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In the equation ax^2 + bx + c = 0, where a, b and c are constants and a ≠ 0, what is the value of b?
(1) 3 and 4 are roots of the equation.
(2) The product of the roots of the equation is 12.
(1) 3 and 4 are roots of the equation.
(2) The product of the roots of the equation is 12.
02 Feb 2019, 01:01
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\(ax^2 + bx + c = 0\)
(1) 3 and 4 are roots of the equation
\((x-3)(x-4) = x^2-7x+12 \rightarrow b= -7\)
\((2x-6)(2x-8) = 4x^2-28x+48 \rightarrow b= -28\)
Not sufficient
(2) The product of the roots of the equation is 12
product of the roots = c/a = 12
Again \(x^2-7x+12 \, and \, 4x^2-28x+48\) are possible
Not sufficient
Combining both the statements
\(x^2-7x+12 \, and \, 4x^2-28x+48\) are possible
Or \(b= -7 \, and \, b= -28\) are possible
Hence E .
(1) 3 and 4 are roots of the equation
\((x-3)(x-4) = x^2-7x+12 \rightarrow b= -7\)
\((2x-6)(2x-8) = 4x^2-28x+48 \rightarrow b= -28\)
Not sufficient
(2) The product of the roots of the equation is 12
product of the roots = c/a = 12
Again \(x^2-7x+12 \, and \, 4x^2-28x+48\) are possible
Not sufficient
Combining both the statements
\(x^2-7x+12 \, and \, 4x^2-28x+48\) are possible
Or \(b= -7 \, and \, b= -28\) are possible
Hence E .
General Discussion
KanishkM
Joined: 09 Mar 2018
Last visit: 18 Dec 2021
Posts: 769
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Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
02 Feb 2019, 00:24
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gmat1393
In the equation ax2 + bx + c = 0, where a, b and c are constants and a ≠ 0, what is the value of b?
(1) 3 and 4 are roots of the equation.
(2) The product of the roots of the equation is 12.
(1) 3 and 4 are roots of the equation.
(2) The product of the roots of the equation is 12.
I believe the question is ax^2 + bx + c = 0
IMO A
from 1, when we know that the roots of the equation are 4 and 3, this means their product will be 12
and we can 12 in 1 way, when b = 7, since both roots are +ive
from 2, now when we know that value of roots is 12,
we can get the product in 2 ways when b=7 or b=-7
making this statement insufficient.
